Seem incensed by the restraint (6)

I believe the answer is:

bridle

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'the restraint' is the definition.
(bridle is a kind of restraint)

I can't explain the remainder of the clue.

(Other definitions for bridle that I've seen before include "Check" , "Bristle" , "Horse restraint" , "Become indignant" , "Bit and reins, etc" .)

I've seen this clue in the Evening Standard.

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